The story of a peacock and a snake

Geometry Level 4

A peacock on a tree of 9 feet height on seeing a snake coming towards its hole situated just below the tree from a distance of 27 feet away from the tree flies to catch it. The peacock after catching it walks back to the hole. If they both possess the same speed, and the ratio of the total distance travelled by the peacock to the distance from the catching point to the tree is in the form of $$\frac{a}{b}$$ where $$a$$ and $$b$$ are co-prime integers, then find $$a+b$$

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